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Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations 被引量:1
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作者 刘希忠 李界通 俞军 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第11期313-319,共7页
Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of t... Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new B?cklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated. 展开更多
关键词 (3+1)-dimensional shallow water wave equation residual symmetry consistent Riccati expansion
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A nonlocal Burgers equation in atmospheric dynamical system and its exact solutions
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作者 xi-zhong liu Jun Yu +1 位作者 Zhi-Mei Lou Xian-Min Qian 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第1期189-194,共6页
From a two-vortex interaction model in atmospheric and oceanic systems, a nonlocal counterpart with shifted parity and delayed time reversal is derived by a simple AB reduction. To obtain some approximate analytic sol... From a two-vortex interaction model in atmospheric and oceanic systems, a nonlocal counterpart with shifted parity and delayed time reversal is derived by a simple AB reduction. To obtain some approximate analytic solutions of this nonlocal system, the multi-scale expansion method is applied to get an AB-Burgers system. Various exact solutions of the AB-Burgers equation, including elliptic periodic waves, kink waves and solitary waves, are obtained and shown graphically.To show the applications of these solutions in describing correlated events, a simple approximate solution for the two-vortex interaction model is given to show two correlated dipole blocking events at two different places. Furthermore, symmetry reduction solutions of the nonlocal AB-Burgers equation are also given by using the standard Lie symmetry method. 展开更多
关键词 AB–BA EQUIVALENCE principle NONLOCAL BURGERS equation periodic waves
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A nonlocal Boussinesq equation:Multiple-soliton solutions and symmetry analysis
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作者 xi-zhong liu Jun Yu 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第5期83-87,共5页
A nonlocal Boussinesq equation is deduced from the local one by using consistent correlated bang method.To study various exact solutions of the nonlocal Boussinesq equation,it is converted into two local equations whi... A nonlocal Boussinesq equation is deduced from the local one by using consistent correlated bang method.To study various exact solutions of the nonlocal Boussinesq equation,it is converted into two local equations which contain the local Boussinesq equation.From the N-soliton solutions of the local Boussinesq equation,the N-soliton solutions of the nonlocal Boussinesq equation are obtained,among which the(N=2,3,4)-soliton solutions are analyzed with graphs.Some periodic and traveling solutions of the nonlocal Boussinesq equation are derived directly from the known solutions of the local Boussinesq equation.Symmetry reduction solutions of the nonlocal Boussinesq equation are also obtained by using the classical Lie symmetry method. 展开更多
关键词 nonlocal Boussinesq equation N-soliton solution periodic waves symmetry reduction solutions
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Dust acoustic waves in collisional uniform dense magnetoplasma
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作者 Jian-Rong Yang Ting Xu +2 位作者 Jie-Jian Mao Ping liu xi-zhong liu 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第1期298-303,共6页
In order to study the characteristics of dust acoustic waves in a uniform dense dusty magnetoplasma system, a nonlinear dynamical equation is deduced using the quantum hydrodynamic model to account for dust–neutral c... In order to study the characteristics of dust acoustic waves in a uniform dense dusty magnetoplasma system, a nonlinear dynamical equation is deduced using the quantum hydrodynamic model to account for dust–neutral collisions. The linear dispersion relation indicates that the scale lengths of the system are revised by the quantum parameter, and that the wave motion decays gradually leading the system to a stable state eventually. The variations of the dispersion frequency with the dust concentration, collision frequency, and magnetic field strength are discussed. For the coherent nonlinear dust acoustic waves, new analytic solutions are obtained, and it is found that big shock waves and wide explosive waves may be easily produced in the background of high dusty density, strong magnetic field, and weak collision. The relevance of the obtained results is referred to dense dusty astrophysical circumstances. 展开更多
关键词 dusty magnetoplasma quantum hydrodynamic model dust acoustic wave
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Multiple soliton solutions and symmetry analysis of a nonlocal coupled KP system 被引量:1
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作者 xi-zhong liu Jie-tong Li Jun Yu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2023年第8期69-77,共9页
A nonlocal coupled Kadomtsev–Petviashivili(ncKP) system with shifted parity(P_(s)^(x)) and delayed time reversal(T_(d)) symmetries is generated from the local coupled Kadomtsev–Petviashivili(cKP) system. By introduc... A nonlocal coupled Kadomtsev–Petviashivili(ncKP) system with shifted parity(P_(s)^(x)) and delayed time reversal(T_(d)) symmetries is generated from the local coupled Kadomtsev–Petviashivili(cKP) system. By introducing new dependent variables which have determined parities under the action of P_(s)^(x)T_(d)^(d), the ncKP is transformed to a local system. Through this way, multiple even number of soliton solutions of the ncKPI system are generated from N-soliton solutions of the c KP system, which become breathers by choosing appropriate parameters. The standard Lie symmetry method is also applied on the ncKPII system to get its symmetry reduction solutions. 展开更多
关键词 nonlocal coupled Kadomtsev-Petviashivili system N-soliton solutions symmetry reduction solutions
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Residual Symmetry Reduction and Consistent Riccati Expansion of the Generalized Kaup-Kupershmidt Equation
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作者 xi-zhong liu Jun Yu +1 位作者 Zhi-Mei Lou Qiao-Jun Cao 《Communications in Theoretical Physics》 SCIE CAS CSCD 2018年第6期625-630,共6页
The residual symmetry of the generalized Kaup-Kupershmidt (KKK) equation is obtained from the truncated Painleve expansion and localized to a Lie point symmetry in a prolonged system. New symmetry reduction solution... The residual symmetry of the generalized Kaup-Kupershmidt (KKK) equation is obtained from the truncated Painleve expansion and localized to a Lie point symmetry in a prolonged system. New symmetry reduction solutions of the prolonged system are given by using the standard Lie symmetry method. Frthermore, the gKK equation is proved to integrable in the sense of owning consistent Riecati expansion and some new Bgcklund transformations are given based on this property, from which interaction solutions between soliton and periodic waves are given. 展开更多
关键词 generalized Kaup-Kupershmidt equation residual symmetry onsistent Riccati expansion
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